The surfaces of real-world objects almost never intersect, so the human visual system is ill prepared to deal with this rare case. However, the comparison of two similar models or approximations of the same surface can require simultaneous estimation of individual global shape, estimation of point or feature correspondences, and local comparisons of shape and distance between the two surfaces. A key supposition of this work is that these relationships between intersecting surfaces, especially the local relationships, are best understood when the surfaces are displayed such that they do intersect. For instance, the relationships between radiation iso-dose levels and healthy and tumorous tissue is best studied in context with all intersections clearly shown. This dissertation presents new visualization techniques for general layered surfaces, and intersecting surfaces in particular, designed for scientists with problems that require such display. The techniques are enabled by a union/intersection refactoring of intersecting surfaces that converts them into nested surfaces, which are more easily treated for visualization. The techniques are aimed at exploratory visualization, where accurate performance of a variety of tasks is desirable, not just the best technique for one particular task. User studies, utilizing tasks selected based on interviews with scientists, are used to evaluate the effectiveness of the new techniques, and to compare them to some existing, common techniques. The studies show that participants performed the user study tasks more accurately with the new techniques than with the existing techniques
